Question

The non-real complex numbers satisfying the equation $z^3+2z^2+3z+2=0$ are

• A. $\frac{-1\pm i\sqrt{7}}{2}$
• B. $-i,\frac{-1\pm \sqrt{7}i}{2}$
• C. $i,\frac{-1\pm \sqrt{7}i}{2}$
• D. $-1,\frac{-1\pm \sqrt{7}i}{2}$

Answer 1

The correct option is A $\frac{-1\pm i\sqrt{7}}{2}$

$z^3+2z^2+3z+2=0$
$z^2(z+1)+(z+1)(z+2)=0$
$(z+1)(z^2+z+2)=0$
$z=-$1 or $z^2+z+2=0$
Hence complex solutions are
$z=\frac{-1\pm \sqrt{1-8}}{2}$
i.e. $z=\frac{-1\pm \sqrt{7}i}{2}$